124 LearnersLast updated on May 26th, 2025
Factors of 243
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 243, how they are used in real life, and tips to learn them quickly.
What are the Factors of 243?
The numbers that divide 243 evenly are known as factors of 243.
A factor of 243 is a number that divides the number without remainder.
The factors of 243 are 1, 3, 9, 27, 81, and 243.
Negative factors of 243: -1, -3, -9, -27, -81, and -243.
Prime factors of 243: 3.
Prime factorization of 243: 35.
The sum of factors of 243: 1 + 3 + 9 + 27 + 81 + 243 = 364
How to Find Factors of 243?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 243. Identifying the numbers which are multiplied to get the number 243 is the multiplication method.
Step 1: Multiply 243 by 1, 243 × 1 = 243.
Step 2: Check for other numbers that give 243 after multiplying
3 × 81 = 243
9 × 27 = 243
Therefore, the positive factor pairs of 243 are: (1, 243), (3, 81), and (9, 27). All these factor pairs result in 243. For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method:
Step 1: Divide 243 by 1, 243 ÷ 1 = 243.
Step 2: Continue dividing 243 by the numbers until the remainder becomes 0.
243 ÷ 1 = 243
243 ÷ 3 = 81
243 ÷ 9 = 27
Therefore, the factors of 243 are: 1, 3, 9, 27, 81, 243.
Prime Factors and Prime Factorization
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 243 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
243 ÷ 3 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factor of 243 is 3. The prime factorization of 243 is: 3^5.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 243 is divided by 3 to get 81
Step 2: Now divide 81 by 3 to get 27.
Step 3: Then divide 27 by 3 to get 9.
Step 4: Divide 9 by 3 to get 3.
Here, 3 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 243 is: 35.
Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.
Positive factor pairs of 243: (1, 243), (3, 81), and (9, 27).
Negative factor pairs of 243: (-1, -243), (-3, -81), and (-9, -27).
Common Mistakes and How to Avoid Them in Factors of 243
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself
For example, in factors of 243, 1 and 243 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 243 include -1, -3, -9, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because 243/1.5 = 162, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 243 are prime numbers. For example, 3 is the prime factor of 243, but it has other factors like 9, 27.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 243 as 3^5 and missing all the key factors.
Factors of 243 Examples
Problem 1
There are 9 teams and 243 marbles. How will they divide them equally?
They will get 27 marbles each.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of teams.
243/9 = 27
Problem 2
A rectangular garden has a length of 27 meters and a total area of 243 square meters. Find the width.
9 meters.
Explanation
To find the width of the garden, we use the formula: Area = length × width
243 = 27 × width
To find the value of the width, we need to shift 27 to the left side.
243/27 = width
Width = 9.
Problem 3
There are 3 shelves and 243 books. How many books will be in each shelf?
Each shelf will have 81 books.
Explanation
To find the number of books in each shelf, divide the total books by the number of shelves.
243/3 = 81
Problem 4
In a class, there are 243 students, and 81 desks. How many students are there per desk?
3 students per desk.
Explanation
Dividing the students by the total desks, we will get the number of students per desk.
243/81 = 3
Problem 5
243 apples need to be packed into 27 boxes. How many apples will go in each box?
Each of the boxes will have 9 apples.
Explanation
Divide total apples by boxes.
243/27 = 9
FAQs on Factors of 243
1.What are the factors of 243?
2.Mention the prime factors of 243.
3.Is 243 a multiple of 9?
4.Mention the factor pairs of 243.
5.What is the cube of 243?
6.How can children in United States use numbers in everyday life to understand Factors of 243?
7.What are some fun ways kids in United States can practice Factors of 243 with numbers?
8.What role do numbers and Factors of 243 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 243 skills?
Important Glossaries for Factors of 243
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 243 are 1, 3, 9, 27, 81, and 243.
- Prime factors: The factors which are prime numbers. For example, 3 is the prime factor of 243.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 243 are (1, 243), (3, 81), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 243 is 35.
- Multiplication method: A method used to find factors by identifying pairs of numbers that multiply to the original number.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
